CAIRO — New signs of instability emerged in Egypt on Monday, just hours after the country’s election commission rejected fraud complaints and confirmed that a conservative Islamist from the Muslim Brotherhood will face off against a secular former military officer in next month’s presidential runoff.

The announcement marked the official start of the second phase of a race in which Egyptian voters will face a stark choice in determining the successor to former president Hosni Mubarak, who was ousted last year.

The Brotherhood’s presidential hopeful, Mohammed Morsi, has called for a more pronounced application of Islamic law. His rival, Ahmed Shafiq, ran on a promise to “neutralize” Islamists and restore security with an “iron fist.”

But in a sign of just how destabilizing the presidential runoff may be, hundreds of men burst into Shafiq’s campaign headquarters on a tree-lined street in the Cairo district of Dokki late Monday and started a fire. Live television images showed the blaze. Witnesses said that the building was intact and that only a few windows were broken from stones being thrown. Supporters of Shafiq rushed to the scene to voice their backing of the former air force commander.

Meanwhile, thousands of demonstrators gathered in Cairo’s Tahrir Square, the birthplace of Egypt’s revolt, to protest the election results and call for the exclusion of Shafiq from the race.

Shafiq and Morsi both took about a quarter of the vote in last week’s first round. Turnout was lower than expected, with 46 percent of registered voters going to the polls.

Election commission head Farouk Sultan told reporters in a news conference Monday that accusations of fraud were thrown out because of a lack of evidence. He said the runoff would proceed despite allegations from other candidates that security officers were unlawfully allowed to vote, in order to swing the balance in favor of Shafiq, who is perceived to have the backing of the ruling military council.

“It’s the most divisive outcome possible,” said Michael Wahid Hanna, an Egypt expert at the Century Foundation. “It’s unfortunate because it was a fragmented field that allowed for a polarized outcome like this.”

There were 13 contenders on the ballot in the first round. The three who finished behind Morsi and Shafiq — former Arab League chief Amr Moussa, Arab Nationalist Hamdeen Sabbahi and progressive Islamist Abdel Moneim Aboul Fotouh — together took about 200,000 more votes than the top two contenders. The results reflect deep divisions in the country more than a year after a revolution that ended Mubarak’s 29-year reign.

Voter turnout for the runoff, which is scheduled for June 16 and 17, probably will be even lower than the showing during the first round of presidential voting, analysts said.

Although the Brotherhood swept the parliamentary vote, the results from last week’s presidential contest show a backlash against the group. The coastal city of Alexandria voted overwhelmingly for Islamists in the parliamentary balloting. But Sabbahi, the only secular front-runner with no links to Mubarak’s government, received the most presidential votes in the city, the country’s second largest.

Many Egyptians have vowed to stay away from the polls during the runoff rather than choose between an Islamist and a candidate many feel is against the revolution. Shafiq has called Mubarak his role model and has suggested in television interviews and public appearances that he has no qualms about using the full force of the state against dissidents.

The losing candidates continued to cry foul Monday. Aboul Fotouh, who was once a Brotherhood leader but severed ties with the organization to run for president, said he would seek to have the election suspended because of electoral violations.

He implied that Shafiq voters were paid and said that ballot boxes had been tampered with.

Moussa, the former foreign minister and ex-Arab League chief, struck a somber note Monday.

“I will stand with all citizens to push Egypt forward and to participate in healing the problems and rebuilding the country,” he said. “I cannot accept the reproduction of the old regime. There has to be a new system based on freedom, based on democracy and based on freedom of opinion, freedom of worship, freedom of scientific research and creativity.”

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